If you suspect that something dishonest or unpleasant has been done, you believe that it has probably been done. If you suspect someone of doing an action of this kind, you believe that they probably did it.

He suspected that the woman staying in the flat above was using heroin. [VERB that]

Police said they suspected that Sobhraj had accomplices. [VERB that]

It was perfectly all right, he said, because the police had not suspected him of
anything. [VERB noun + of]

You don't really think Webb suspects you? [VERB noun]

Frears was rushed to hospital with a suspected heart attack. [VERB-ed]